Principal Component Analysis

Principal Component Analysis (PCA) is a dimensionality reduction technique. It converts high-dimensional data into fewer dimensions. PCA retains most of the original information while simplifying the data. Useful for visualization, noise reduction, and feature extraction.

Why Use PCA?

• To reduce complexity in data analysis.

• To improve performance of machine learning models.

• To remove multicollinearity between variables

• To visualize high-dimensional data in 2D or 3D

Steps in Performing PCA

• Standardize : Standardize the data.

• Calculate : Calculate the covariance matrix.

• Compute : Compute eigenvalues and eigenvectors.

• Select principal components based on eigenvalues.

• Project Project data onto principal components

Key Terminologies

• Covariance Matrix: Shows the relationship between variables.

• Eigenvectors: Directions of the new feature space.

• Eigenvalues: Magnitude of variance captured by each principal component.

• Principal Components: Linear combinations of original features

Applications of PCA

• Image compression and recognition.

• Financial data analysis

• Bioinformatics and genetics

• Pattern recognition and signal processing

• Preprocessing step in ML pipelines.

Visualizing PCA

• PCA Helps Reduce Data To 2 Or 3 Dimensions For Plotting

• Commonly Used For Clustering Or Classification Visualization

• Each Point Is A Projection On The Principal Components